We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure. Moreover, the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Central Limit Theorem.
We consider open sets of maps in a manifold M exhibiting non-uniform expanding behaviour in some domain S ⊂ M . Assuming that there is a forward invariant region containing S where each map has a unique SRB measure, we prove that under general uniformity conditions, the SRB measure varies continuously in the L 1 -norm with the map.As a main application we show that the open class of maps introduced in [V] fits to this situation, thus proving that the SRB measures constructed in [A] vary continuously with the map.
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